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Asymptotic Approximations of Ratio Moments Based on Dependent Sequences

Author

Listed:
  • Hongyan Fang

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Saisai Ding

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Xiaoqin Li

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Wenzhi Yang

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

Abstract

The widely orthant dependent (WOD) sequences are very weak dependent sequences of random variables. For the weighted sums of non-negative m -WOD random variables, we provide asymptotic expressions for their appropriate inverse moments which are easy to calculate. As applications, we also obtain asymptotic expressions for the moments of random ratios. It is pointed out that our random ratios can include some models such as change-point detection. Last, some simulations are illustrated to test our results.

Suggested Citation

  • Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:361-:d:329554
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    References listed on IDEAS

    as
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    5. Xuejun Wang & Yi Wu & Shuhe Hu, 2016. "Exponential probability inequality for $$m$$ m -END random variables and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 127-147, February.
    6. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    7. Wu, Tiee-Jian & Shi, Xiaoping & Miao, Baiqi, 2009. "Asymptotic approximation of inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1366-1371, June.
    8. Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    9. Aiting Shen & Yu Zhang & Benqiong Xiao & Andrei Volodin, 2017. "Moment inequalities for m-negatively associated random variables and their applications," Statistical Papers, Springer, vol. 58(3), pages 911-928, September.
    10. Liu, Li, 2009. "Precise large deviations for dependent random variables with heavy tails," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1290-1298, May.
    11. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    12. Wenzhi Yang & Zhangrui Zhao & Xinghui Wang & Shuhe Hu, 2017. "The large deviation results for the nonlinear regression model with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 261-283, June.
    13. Shi, Xiaoping & Wu, Yuehua & Liu, Yu, 2010. "A note on asymptotic approximations of inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1260-1264, August.
    14. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
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    Cited by:

    1. Michal Pešta, 2021. "Changepoint in Error-Prone Relations," Mathematics, MDPI, vol. 9(1), pages 1-25, January.
    2. Mantas Dirma & Saulius Paukštys & Jonas Šiaulys, 2021. "Tails of the Moments for Sums with Dominatedly Varying Random Summands," Mathematics, MDPI, vol. 9(8), pages 1-26, April.

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